Click here for a printable tangent construction worksheet
This demonstration shows how to construct the
tangent to a given circle through a given point
on the circle using only a compass and straight edge.
See "Introduction to Constructions".
We start with a given circle with center O and a point P on the circle. The result is the tangent line that passes through P.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
Step-by-step Instructions
| Step 1 |
Draw a straight line through the center O of the circle and the point P right across the circle.
This is a diameter of the circle. |
| Step 2 |
Mark a point Q anywhere. For best accuracy, avoid putting it too close to the diameter line. |
| Step 3 |
Place the compass on the point Q just drawn, and set it's width to the point P. |
| Step 4 |
Without changing the width, draw an arc across the diameter line, creating point R. |
| Step 5 |
Without changing its width, draw another arc on the opposite side of Q. |
| Step 6 |
Using the straightedge, draw a line through R and Q, extending it onwards so it crosses the arc just drawn. Mark this point S. |
| Step 7 |
Using the straightedge, draw a line through P and S, extending it in both directions. |
| Step 8 |
Done. The line just drawn is the tangent to the circle O through point P. |
How it works
Recall that the tangent to a circle is perpendicular to the radius at the contact point. (See
Tangent definition page).
This construction uses that fact in reverse. By constructing a line at right angles to the diameter it must be the tangent line.
The method used to construct the perpendicular is exactly the same as the one used in
"Construct a perpendicular at the end of a ray".
Try it yourself
Click here for a printable tangents construction worksheet with some problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page